Solutions and Periodic Solutions for Nonlinear Evolution Equations with Non-Monotone Perturbations

Abstract

In this paper we solve periodic and Cauchy problems for nonlinear evolution equa-tions driven by time-dependent, pseudomonotone operators and a non-monotone perturbation term. Our proof produces as a by-product a useful property of the solution map for maximal monotone problems. Two examples of nonlinear parabolic problems illustrate the applicability of our work.